Application of Response Spectrum Analysis of Multiply Supported System, with the Multi-Directional Excitations and Residual Rigid Response

In the seismic design of equipment and piping systems, it seems that the precise response spectrum analysis method of multiply supported systems with good accuracy does not spread, though there are many multiply supported systems which subject the different earthquake excitations. The Standard Review Plan 3.7.1 in the United States, for example, recommends that the seismic response of each support point be combined by the absolute sum. However, this leads to excessive conservative seismic response, and there is a problem in the analytical accuracy. Then, this paper presents a basic equation of motion of a multiply supported systems considering correlation between modes and seismic excitation directions and residual rigid response of a multiply supported system receiving three-directional earthquake excitations of X, Y and Z. The correlation of the multiply supported system response is applied to the CCFS method based on the sophisticated random vibration theory by Kiureghian, the residual rigid response is based on the missing mass method on the Regulatory Guide 1.92 Rev.2, and the synthesis method of the multi-directional earthquake excitations is based on our previous work, The purpose of this paper is to present a precise analytical evaluation formula for the multiple response spectrum analysis method and to hope to promote the improvement of the design guidelines for multiply supported equipment and piping systems.